Question: Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-5x+y &= -1 \\ 9x-9y &= 5\end{align*}$
Begin by moving the $y$ -term in the second equation to the right side of the equation. $9x = 9y+5$ Divide both sides by $9$ to isolate $x$ $x = {y + \dfrac{5}{9}}$ Substitute this expression for $x$ in the first equation. $-5({y + \dfrac{5}{9}}) + y = -1$ $-5y - \dfrac{25}{9} + y = -1$ Simplify by combining terms, then solve for $y$ $-4y - \dfrac{25}{9} = -1$ $-4y = \dfrac{16}{9}$ $y = -\dfrac{4}{9}$ Substitute $-\dfrac{4}{9}$ for $y$ in the top equation. $-5x- \dfrac{4}{9} = -1$ $-5x-\dfrac{4}{9} = -1$ $-5x = -\dfrac{5}{9}$ $x = \dfrac{1}{9}$ The solution is $\enspace x = \dfrac{1}{9}, \enspace y = -\dfrac{4}{9}$.